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Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $\sigma_1(G)<\frac{117}{20}$, then $G$ is sol\-va\-ble. This partially solves an open problem posed in \cite{9}.
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참고문헌 (9)
참고문헌 신청
S. M. J. Amiri / 2013 / Characterization of A5 and PSL(2; 7)by sum of element orders / Int. J. Group Theory 2(2):35~39
Morteza Baniasad Azad / 2018 / A criterion for solvability of a finite group by the sum of element orders / Journal of Algebra 516:115~124
V A Belonogov / 1988 / FINITE GROUPS WITH THREE CLASSES OF MAXIMAL SUBGROUPS / Mathematics of the USSR-Sbornik 59(1):223~236
L. E. Dickson / 1958 / Linear groups with an exposition of the Galois field theory, with an intro-duction by W. Magnus / Dover Publications, Inc
Marcel Herzog / 2018 / Two new criteria for solvability of finite groups / Journal of Algebra 511:215~226
Morteza Baniasad Azad / 2018 / A criterion for solvability of a finite group by the sum of element orders / Journal of Algebra 516:115~124
V A Belonogov / 1988 / FINITE GROUPS WITH THREE CLASSES OF MAXIMAL SUBGROUPS / Mathematics of the USSR-Sbornik 59(1):223~236
L. E. Dickson / 1958 / Linear groups with an exposition of the Galois field theory, with an intro-duction by W. Magnus / Dover Publications, Inc
Marcel Herzog / 2018 / Two new criteria for solvability of finite groups / Journal of Algebra 511:215~226
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